• # Curriculum

This course is organized into nine units with an course closure project at the end of the course.
For each unit, there is core content which is completed by students using a combination of whole class instruction; discussion;  and team investigations and practice.  A test on this core content is worth 80% of the unit assessment.  At the end of the core instruction, students will have time to complete enrichment activities that allow students to learn content of choice at a deeper level.  These activites are worth 20% with a 5% bonus opportunity.  Students are expected to complete activities in categories of:  remediation, instructional resource, historical research, applications, graphical thinking and data analysis, investigation and proof, writing about concepts, and potpourri.  Each semester students are required to complete between 1 to 3 activities from each category.

### Content of Units:

Limits and Continuity
• Finding limits graphically, numerically, and analytically
• Studying continuity and one sided limits
• Infinite limits
Differentiation Part 1
• Definition of derivative as both slope of tangent line and limit defintion
• Basic differentiation rules and rates of change
• Product and Quotient rules for derivatives
• Higher order derivatives
Differentiation Part 2
• Chain Rule
• Implicit Differentiation
• Related Rates
Application of Differentiation Part 1
• Extrema on an interval
• Increasing and decreasing functions with first derivative test
• Concavity and the second derivative test
• Limits at infinity with horizontal asymptotes
Application of Differentiation Part 2
• Analysis of a function using the derivative function
Application of Differentiation Part 3
• Rolle's Theorem and Mean Value Theorem
• Optimization Problems
• Newton's Method
• Differentials
Integration
• Integration as the antiderivative and indefinite integrals
• Integration as the area under a curve and definite integrals
• The fundamental theorem of calculus
• Integration by substitution
• Numerical integration
Differential Equations
• Integration and differentiation of exponential function
• Integration and differentiation of the natural logarithmic function
• Slope fields and Euler's method
• Differential Equations:  Growth and Decay
• Separation of Variables and the Logistic equation
• First order linear differential equations
Applications of Integration
• Area of region between two curves
• The disk method of volume
• The shell method of volume

Various course closure activites will be offered during the last several weeks of school.